The perimeter of the norwegian flag is 190 inches
1 answer:
You might be interested in
Answer:
Domain and Range
Step-by-step explanation:
Let be the given function
Function:
Function can be defined as "A special relationship where each input has a single output".
It is often written as "" where x is the input value.
Domain:
The domain of a function is the complete set of possible values of the independent variable.
Range:
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Function is the set of all ordered pairs of domain and range. It can be written as
where
are domain and
are range
Given the ordered pairs of domain and range where
are domain and
are range.
ie, Domain and Range
The graph of the given function is attached showing characteristics of the function.
The correct responses are;
- (a) F'(4) = -30 means that <u>on day 4, the number of fish in the bay is decreasing at a rate of 30 fish per day</u>.
- (b) Over the interval 0 ≤ t ≤ 8 the absolute minimum number of fish in the bay is;<u> 1,000</u>.
- (c) The values of <em>t</em> at which the rate of change is decreasing is; <u>3 ≤ t ≤ 8</u>
- (d) The rate of change of the number of pelicans flying near is; P' = <u>10·(3·c² - 24·c + 45)</u>
Reasons:
The given function is; f(t) = 10·(t³ - 12·t² + 45·t + 100)
Where;
t = Number of days
0 ≤ t ≤ 8
(a) The derivative of the given function is presented as follows;
F'(t) = 10 × (3·t² - 2×12·t + 45) = 10·(3·t² - 24·t + 45)
Therefore;
F'(4) = 10 × (3 × 4² - 24 × 4 + 45) = -30
Therefore F'(4) = -30 means that on day 4, the <u>number of fish in the bay is decreasing at 30 fish per day</u>.
(b) The absolute minimum is given as follows;
At a minimum or maximum value, F'(t) = 10·(3·t² - 24·t + 45) = 0
Which gives;
3·(t - 5)·(t - 3) = 0
t = 5, or t = 3
At t = 5, we have;
f(5) = 10 × (5³ - 12 × 5² + 45 × 5 + 100) = 1,500
At t = 3, we have;
f(3) = 10 × (3³ - 12 × 3² + 45 × 3 + 100) = 1,540
Therefore, f(5) = 1,500 is a local maximum
However, at x = 0, we have;
f(0) = 10 × (0³ - 12 × 0² + 45 × 0 + 100) = 1000
At x = 8, we have;
f(8) = 10 × (8³ - 12 × 8² + 45 × 8 + 100) = 2,040
Therefore, the absolute minimum is given at t = 8, where f(t) = <u>1,000</u>
(c) The values of <em>t</em> at which the rate of change in the number of fish in the
bay is decreasing is between the local maximum at t = 3, and the local
minimum at t = 5, which gives;
The rate of change of the number of fish is decreasing for values of t in the range;
- <u>3 ≤ t ≤ 5</u>
(d) P = 10·(t³ - 12·t² + 45·t + 100)
P' = 10·(3·t² - 24·t + 45)
At time t = c, we have;
- P' = 10·(3·c² - 24·c + 45)
<em>Based on a similar question online, we have;</em>
<em>(c) The interval over which the rate of change is decreasing</em>
<em>(d) The rate of change of the number of pelicans flying near the bay at t = c</em>
Learn more about differentiation of functions here:
